From Dependence to Causation

Machine learning is the science of discovering statistical dependencies in data, and the use of those dependencies to perform predictions. During the last decade, machine learning has made spectacular progress, surpassing human performance in complex tasks such as object recognition, car driving, and computer gaming. However, the central role of prediction in machine learning avoids progress towards general-purpose artificial intelligence. As one way forward, we argue that causal inference is a fundamental component of human intelligence, yet ignored by learning algorithms. Causal inference is the problem of uncovering the cause-effect relationships between the variables of a data generating system. Causal structures provide understanding about how these systems behave under changing, unseen environments. In turn, knowledge about these causal dynamics allows to answer "what if" questions, describing the potential responses of the system under hypothetical manipulations and interventions. Thus, understanding cause and effect is one step from machine learning towards machine reasoning and machine intelligence. But, currently available causal inference algorithms operate in specific regimes, and rely on assumptions that are difficult to verify in practice. This thesis advances the art of causal inference in three different ways. First, we develop a framework for the study of statistical dependence based on copulas and random features. Second, we build on this framework to interpret the problem of causal inference as the task of distribution classification, yielding a family of novel causal inference algorithms. Third, we discover causal structures in convolutional neural network features using our algorithms. The algorithms presented in this thesis are scalable, exhibit strong theoretical guarantees, and achieve state-of-the-art performance in a variety of real-world benchmarks.